Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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Name for space of piecewise continuous functions

The space of $k$ times continuously differentiable functions (on $\mathbb R$) is called $C^k$. Is there a similar name for functions that are piecewise continuous? For example the box function ...
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1answer
28 views

Terminology for splittings of a set into two parts

I have a set of values $V$ that can be split by any combination $C$ of the elements $v$ that belongs to $V$. Order is not important and repetitions are not allowed. For example, $V := \{1,2,3,4\}$ ...
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2answers
65 views

If $f(x) = 0$ has a countable set of solutions, what is $f$?

Is there a name given to functions $f$, where the roots of $f(x) = 0$ are countable? I am assuming $f$ is a real function of a real variable, $x$.
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1answer
361 views

Sign Language and Deaf Mathematicians

Something I've often wondered (and I suppose this goes for all kinds of technical terminology, not just that of mathematics) is what kind of sign language exists for practising professional ...
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1answer
28 views

Help in this teminology in Hartshorne's algebraic geometry book

I'm studying Hartshorne's Algebraic Geometry book and on page 51: What the author means by $M_{\mathfrak p}$ and "length"? I suppose $S_{\mathfrak p}$ is the localization of the ring $S$ at ...
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1answer
12 views

Splitting of primes terminology doubt

What do we mean when we say that a given prime $p$ splits completely in an algebraic extension of $\mathbb Q$? Are we talking about the splitting of prime ideals into unique factors? And, in that ...
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1answer
30 views

Are pairwise mutually exclusive events the same as mutually exclusive events?

Larson (1982) defining the probability axioms talks about "mutually exclusive" events, while Poirier (1995) about "$A_1, A_2, \ldots$ as a sequence of pairwise mutually exclusive events events in the ...
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1answer
73 views

Question about terminology in number theory

The following transformation appears often in number theory: $$F(x) = \sum_{n \le x} f \left( \frac{x}{n} \right)$$ What is the name of this transformation? PS. I will accept as answer something ...
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1answer
123 views

What is the origin of the terms 'jet' and 'prolongation' in differential geometry?

I am just curious what is the reason for the terms 'jet' and 'prolongation' in differential geometry? Is there some mental imagery that these names are supposed to evoke? Or are they so-named because ...
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0answers
30 views

What should you call a property, like an invariant, but that is reversed instead of preserved?

Suppose $P$ is some property of some objects and $f$ is a function on those objects. If $Px$ implies $Pf(x)$ and $\lnot Px$ implies $\lnot Pf(x)$, then we might say that "$P$ is invariant under $f$". ...
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1answer
37 views

Labeled commutative diagram

Consider a commutative diagram. For example the following diagram in $\mathbf{Set}$: $$ \begin{array}{ccc} & \overset{+1}{\longrightarrow} &\\ \mathbb{Z} & & \mathbb{Z} \\ & ...
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1answer
62 views

What's the meaning of “drop” in mathematics?

What's the meaning of "drop" in following sentence: "the term can be dropped from the numerator"
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0answers
53 views

An endomorphism $f$ such that $f\circ f=1$

What is the name for an endomorphism $f$ of a category such that $f\circ f=1$? Note that I work with category $\mathbf{Set}$.
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1answer
82 views

Is $\mathbb{Z}/p^\mathbb{N} \mathbb{Z}$ widely studied, does it have an accepted name/notation, and where can I learn more about it?

Fix a positive integer $p$, possibly prime. For each natural number $n$, there is a ring $\mathbb{Z}/p^n \mathbb{Z}$ together with a distinguished ring homomorphism $$\pi_n:\mathbb{Z} \rightarrow ...
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2answers
157 views

Is there a formal definition for antiderivatives?

In the way the derivative can be defined as a limit, specifically $$f'(x):=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ or any of the other possible variants, is there a way to define the antiderivative, as in ...
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1answer
19 views

Does the operand in a convolution have a particular name?

In a convolution: $$(f*g*h)(t) = \int f(x)g(y)h(z) \delta(t-x-y-z) dxdydz$$ do the operands $f,g,h$ have a specific name, besides the general "operand"?
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1answer
46 views

What is the scientific term form something that 'wraps around' a shape

I was wondering if there is a mathematical term for this: Imagine you had given the black shape - what does the red shape? I would call it, it wraps around the black one. Actually I am looking ...
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1answer
20 views

What does “decreases more slowly” mean mathematically with regard to distributions?

In a paper I'm reading, the authors state that a certain distribution "decreases more slowly than exponentially over a portion of the range". What does this mean, mathematically? Assuming $A$ is the ...
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1answer
39 views

Wording in English for “quantité conjuguée” in French

In French when you have an expression of the type $\sqrt{x}-\sqrt{y}$, the expression $\sqrt{x}+\sqrt{y}$ is named the "quantité conjuguée". This is useful when you want to bound $$\vert ...
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0answers
43 views

The definitions of “transformation” and “isometry”

Let $T$ be a mapping from the plane to itself. In the context of Euclidean geometry, can $T$ be called a "transformation", or is this word reserved for cases where $T$ is bijective? Is there ...
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0answers
21 views

Why is equivalence 'class', not equivalence 'set'? [duplicate]

Why do we call it a class, not a set? Is it not a set? Can it be a proper class?
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0answers
24 views

What are these algebraic properties called?

Suppose $O$ is some operator, suppose $f$ and $g$ are both functions, then linearity implies that: $O(\alpha f + g) = \alpha O(f) + O(g)$ What about the following property: $(O_1+O_2)(f) = O_1(f) ...
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1answer
32 views

Is there a mathematical distinction between “on” and “in”?

Is there any difference if I said a function on an interval or a function in an interval? or a vector field on a manifold versus a vector field in a manifold? The main reason is because some online ...
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0answers
14 views

Definition of (minimal) domain?

Consider the following links: http://www.glottopedia.org/index.php/Domain_%28Syntax%29 http://www2.let.uu.nl/uil-ots/lexicon/zoek.pl?lemma=Minimal+domain&lemmacode=542 What kind of mathematical ...
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1answer
46 views

Why the spatial/mathematician's Fourier Transform?

I was wondering why the sign-change in the exponential of the spatial/mathematician's Fourier Transform and why is it called mathematician's spatial in either case?
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1answer
38 views

What is $D(n,k)$? (dee-en-kay) /ˈdiːˈɛnˈkeɪ/

Is this combinations with repetitions, i.e. ${n+k-1\choose k-1}$ or is this something else entirely? I see this a lot, but with this kind of language no search engine is going to help. The edit in ...
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1answer
798 views

Is there a term for the ratio of a function and its derivative?

Given a function $f(x)$ and its derivative $f'(x)$, is there a term for $\frac{f(x)}{f'(x)}$ or for $\frac{f'(x)}{f(x)}$?
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0answers
25 views

Are the names such as $N_1$-space, $N_2$-space used for various countability axioms

In this question the OP mentioned "$N_i$-hierarchy for various countability axioms and also that the name $N_2$-space or $N_2$-property is used for second countable space. I did not encounter this ...
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3answers
126 views

What is the significance of stuff like the “Pigeonhole Principle”? [closed]

Pigeonhole Principle if n items are put into m containers, with n > m, then at least one container must contain more than one item src I thoroughly read What is your favorite application of the ...
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14answers
2k views

Name of the highest power of 2 smaller than or equal to a given number

For a number $x$, I would like to know whether there is a common name for the number $2^n$ such as $2^n \leq x < 2^{n+1}$ (e.g. If $x = 7$, then $2^n = 4$, $n = 2$). I have some computer science ...
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0answers
38 views

What is $\Bbb E$? Is is $\Bbb R$ with the standard Euclidean topology?

What is $\Bbb E$? I believe this is just alternative notation for $\Bbb R$ where $\Bbb R$ is assumed to have the standard Euclidean topology. Is this correct? Is seems to be used in this way in ...
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1answer
33 views

Terminology: name for integer “factor” of a rectangle?

Basic terminology question from a non-mathematician. I started trying to express this with mathematical terms, but decided any potential errors might be more frustrating than the imprecision of ...
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1answer
26 views

What is axiomatic method? Does it mean giving definitions beforehand and then using them in the proofs?

Also, what does axiomatic approach to probability mean? Does it mean a similar thing?
5
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1answer
69 views

Why did Euclid name his book as “Elements”. What does “element” mean in this context?

Does it relate to the nature of the book in some way?
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1answer
56 views

How do you pronounce Richard Courant's surname?

Since his surname looks rather French than German, I started wondering how you pronounce his name. In particular, I'd be interested in how he would have pronounced his name himself (since I already ...
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2answers
100 views

Why are Natural Numbers called Natural Numbers?

When we say $1,2,3...$ are natural numbers, why don't we include rational and irrational numbers? Isn't $\pi$ something natural? Shouldn't we say all real numbers the Natural numbers? Shouldn't ...
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0answers
21 views

Is it customary to call it “R-module ring homomorphism”?

Let $R$ be a ring. Let $M,N$ be rings together with $R$-module structures, but $M,N$ are not $R$-algebras Let $\phi:M\rightarrow N$ be a ring homomorphism which is also an $R$-module homomorphism. ...
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1answer
11 views

Understanding terminology related to implementing the sobel edge detection algorithm

I'm trying to follow a scholarly paper that discusses a modified implementation of the sobel edge detection algorithm, but I'm not following the terminology 100%. The Sobel detector consists of ...
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4answers
116 views

I call them squares. They called them arrays. What do they mean?

So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that ...
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0answers
23 views

What's the name of this tensor product?

Fix $V$ to be a vector space over $\mathbb{R}$. For all $k \in \mathbb{N}$, let $L_k$ be the space of all $k$-tensors on $V$, and let $S_k$ be the set of all permutations of the set $\{1,\dots, k\}$. ...
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3answers
68 views

Is zero “finite” - Terminology

edit: This is usually done by physicists, engineers, etc. And it refers to a numerical value, not a set. It is used for cases the numerical value of $0$ is not allowed as well. Infinity, is clearly ...
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3answers
820 views

Why lower case “a” for “abelian group” and upper case “C” for “Cauchy sequence”?

This has been bugging me. Why is the lower case letter "a" used to spell "abelian group" when upper case letters are used to spell the terms, "Gaussian Integral", "Cantor set" or "Cauchy ...
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1answer
51 views

Mathematical symbol for Symbolic Replacement

(Posted at mathematica.SE, as it might be better there) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
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2answers
44 views

What type of angle is $3+ \frac{1}{6}$ of a complete rotation?

Angle less than $90$ deg is acute, angle greater than $90$ and less than $180$ is obtuse and angle greater than $180$ deg is reflex. Now, what if an angle is a $3+\frac{1}{6}$ of a complete rotation? ...
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6answers
1k views

What is an adjective for “weaker than weak”?

I defined a notion (say, some kind of equivalence) in three forms, the first implies the second, which in turn implies the third. I would like to use "strong", (nothing), and "weak" to describe them. ...
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1answer
29 views

What does “2- place real function” mean?

What does "2-place real function" mean? This comes up in the context of copulas, as here.
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1answer
83 views

Origin of the term dual space?

Basically, why is a dual vector space called as such? Is the reason for the term "dual" simply because the two vector spaces are related by a one-to-one mapping, or is there something more to it? ...
2
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1answer
104 views

What is the name of this geometric shape?

#1 I am trying to find the name for this when $d1 = d2$ What is the name of this object? #2 Assume d1 is different than d2. What is the name of this kind of object?
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6answers
333 views

What is the significance of using “$a$” vs “$x$” in this text?

I'm a web development guy currently learning Calculus and am having some trouble understanding the seemingly unwritten rules of variable naming conventions in mathematics. I've read several other ...
2
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0answers
34 views

Relation of ideals in probability with other kinds of ideals?

It seems that there are at least 5 kinds of ideals in maths: Ideals in number theory (Kummer, Dedekind) Ideals in abstract algebra (Dedekind, Noether), as kernels of homomorphisms Ideals in order ...